Fragment of nonstandard analysis with a finitary consistency proof

Abstract

We introduce a nonstandard arithmetic NQA⁻ based on the theory developed by R. Chuaqui and P. Suppes in [2] (we will denote it by NQA⁺), with a weakened external open minimization schema. A finitary consistency proof for NQA⁻ formalizable in PRA is presented. We also show interesting facts about the strength of the theories NQA⁻ and NQA⁺; NQA⁻ is mutually interpretable with IΔ₀+EXP, and on the other hand, NQA⁺ interprets the theories IΣ₁ and WKL₀.